definitions.tex

% General Math Notation
\def\vct#1{\bm{#1}}  % vectors in bold
\def\trans{\intercal}  % matrix transpose symbol

% Our Method
\def\ours{\textit{blinx}\xspace}
\def\lbfcs{{lbFCS+}\xspace}
\def\qpaint{{qPAINT}\xspace}
\def\hmm{hidden Markov model\xspace}

% Variables
\def\n{\ensuremath{n}\xspace}                 % count
\def\ndist{\ensuremath{\vct{n}}\xspace}       % distribution of predictions
\def\truen{\ensuremath{n^*}\xspace}           % true count
\def\estimatedn{\ensuremath{\hat{n}}\xspace}  % estimated count
\def\z#1{\ensuremath{z_{#1}}\xspace}          % number of active emitters at time t: \y{t}
\def\x#1{\ensuremath{x_{#1}}\xspace}          % intensity at time t: \x{t}
\def\xp#1{\ensuremath{\tilde{x}_{#1}}\xspace} % intensity at time t in photon space: \xp{t}
\def\states{\ensuremath{\vct{z}}\xspace}      % all active emitters over time
\def\trace{\ensuremath{\vct{x}}\xspace}       % all intensities over time
\def\pon{\ensuremath{p_\text{on}}\xspace}     % prob. for activating
\def\poff{\ensuremath{p_\text{off}}\xspace}   % prob. for deactivating
\def\re{\ensuremath{r_e}\xspace}              % fluorophore emission rate
\def\rb{\ensuremath{r_b}\xspace}              % background emission rate
\def\camoffset{\ensuremath{\mu}\xspace}       % camera offset
\def\camvar{\ensuremath{\sigma^2}\xspace}     % camera variance
\def\camgain{\ensuremath{g}\xspace}           % camera gain
\def\parameters{\ensuremath{\theta}\xspace}   % all parameters (mu, sigma, ...)
\def\parameterst{\ensuremath{\parameters_T}\xspace}  % transition parameters
\def\parameterse{\ensuremath{\parameters_E}\xspace}  % emission parameters
\def\parametersc{\ensuremath{\parameters_C}\xspace}  % camera parameters
\def\parametersmap{\ensuremath{\theta}_\text{MAP}\xspace}   % MAP solution of parameters
\def\photons{\ensuremath{c}\xspace}           % number of photons per spot
\def\deltat{\ensuremath{\Delta t}\xspace}     % length of frame

\def\pchain{\ensuremath{\alpha\xspace}}       % recursive probability for forward algorithm
\def\pchainnorm{\ensuremath{\tilde{\alpha}\xspace}}
                                              % \pchain normalized
\def\norms{\ensuremath{\beta\xspace}} % normalization factors for \pchain
\def\object{object\xspace} % what to call things we want to count
\def\objects{objects\xspace} % what to call things we want to count plural
\def\smallobjects{subunits\xspace} % what to call things we want to count plural

\DeclareMathOperator{\poisson}{Poisson}

% units
\def\micrometer{\unit{\micro\meter}\xspace}
\def\nanometer{\unit{\nano\meter}\xspace}

% Functions
%\newcommand{\argmax}[1]{\mathop{\arg\max}_{#1}\hspace{0.5em}}